Theorems · Theorem · group theory
DirectSum.sum_support_of
∀ {ι : Type v} {β : ι → Type w} [inst : (i : ι) → AddCommMonoid (β i)] [inst_1 : DecidableEq ι]
[inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] (x : DirectSum ι fun i => β i),
∑ i ∈ DFinsupp.support x, (DirectSum.of β i) (x i) = x- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- AddMonoidHomstatement · cited by 3,230
- DFinsuppstatement · cited by 694
- DirectSumstatement and proof · cited by 446
- DFinsupp.supportstatement · cited by 158
- DirectSum.ofstatement · cited by 122
- DFinsupp.sum_singleproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.sum_support_decomposeproof · cited by 9